igraph (version 0.4.3)

closeness: Closeness centrality of vertices

Description

Cloness centrality measures how many steps is required to access every other vertex from a given vertex.

Usage

closeness(graph, v=V(graph), mode = "all")

Arguments

graph

The graph to analyze.

v

The vertices for which closeness will be calculated.

mode

Character string, defined the types of the paths used for measuring the distance in directed graphs. in measures the paths to a vertex, out measures paths from a vertex, all uses und

Value

• Numeric vector with the closeness values of all the vertices in v.

Details

The closeness centrality of a vertex is defined by the inverse of the average length of the shortest paths to/from all the other vertices in the graph:

$$\frac{|V|-1}{\sum_{i\ne v} d_vi}$$

If there is no (directed) path between vertex $v$ and $i$ then the total number of vertices is used in the formula instead of the path length.

References

Freeman, L.C. (1979). Centrality in Social Networks I: Conceptual Clarification. Social Networks, 1, 215-239.

See Also

betweenness, degree

Examples

g <- graph.ring(10)
g2 <- graph.star(10)
closeness(g)
closeness(g2, mode="in")
closeness(g2, mode="out")
closeness(g2, mode="all")